Triple transgenic mice generation from different background singles

I am wanting to make a triple transgenic animal model where two of the transgenes (tetO-Cre and tissue specific rtTA) are in FVB/n background and a flox/flox alele is in C57Bl/6.

my initial strategy would be to create Cre/- flox/flox mice and rtTA/- flox/flox mice and cross those to get Cre/- rtTA/- flox/flox mice for experiments. My concern is that the heterogeneity of background in the triple transgenic mice may scatter the data, requiring very high n for significance, and also that I would have to maintain the single transgenics in their original backgrounds to set up equivalent crosses in future experiments.

We have the FVB/n mice currently and are waiting on transfer of the C57 floxed mouse which will have to be re-derived due to a viral infection. Would it be better for me to start outcrossing the Cre and rtTA lines into C57 background for a few generations to eliminate heterogeneity later? Any suggestions are appreciated.

Background heterogeneity is always a problem in multiple knockout animals. As long as you compare littermate controls, you can usually rule out background genetic noise. Because you will have cre+ and cre-, this comparison is possible. The alternative is 10 generations of backcross to stabilize the line genetically. This is expensive and very time consuming.